
/* @(#)k_sin.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/* __kernel_sin( x, y, iy)
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
 *
 * Algorithm
 *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
 *	3. sin(x) is approximated by a polynomial of degree 13 on
 *	   [0,pi/4]
 *		  	         3            13
 *	   	sin(x) ~ x + S1*x + ... + S6*x
 *	   where
 *
 * 	|sin(x)         2     4     6     8     10     12  |     -58
 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
 * 	|  x 					           |
 *
 *	4. sin(x+y) = sin(x) + sin'(x')*y
 *		    ~ sin(x) + (1-x*x/2)*y
 *	   For better accuracy, let
 *		     3      2      2      2      2
 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
 *	   then                   3    2
 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
 */

#include "fdlibm.h"

#ifdef _NEED_FLOAT64

static const __float64
    half = _F_64(5.00000000000000000000e-01), /* 0x3FE00000, 0x00000000 */
    S1 = _F_64(-1.66666666666666324348e-01), /* 0xBFC55555, 0x55555549 */
    S2 = _F_64(8.33333333332248946124e-03), /* 0x3F811111, 0x1110F8A6 */
    S3 = _F_64(-1.98412698298579493134e-04), /* 0xBF2A01A0, 0x19C161D5 */
    S4 = _F_64(2.75573137070700676789e-06), /* 0x3EC71DE3, 0x57B1FE7D */
    S5 = _F_64(-2.50507602534068634195e-08), /* 0xBE5AE5E6, 0x8A2B9CEB */
    S6 = _F_64(1.58969099521155010221e-10); /* 0x3DE5D93A, 0x5ACFD57C */

__float64
__kernel_sin(__float64 x, __float64 y, int iy)
{
    __float64 z, r, v;
    __int32_t ix;
    GET_HIGH_WORD(ix, x);
    ix &= 0x7fffffff; /* high word of x */
    if (ix < 0x3e400000) /* |x| < 2**-27 */
        return __math_inexact(x);       /* generate inexact */
    z = x * x;
    v = z * x;
    r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
    if (iy == 0)
        return x + v * (S1 + z * r);
    else
        return x - ((z * (half * y - v * r) - y) - v * S1);
}

#endif /* _NEED_FLOAT64 */
